The anisotropic diffusion model is simple yet powerful: it already utilizes a significant fraction of the overall numerical capabilities of the code.
\[ \partial_t u = \chi_\parallel\nabla\cdot(\nabla_\parallel u)+\nabla\cdot\left(\chi_\perp\nabla_\perp u\right) \]
Due to the flute mote character of turbulence in magnetised plasmas, i.e. , the dynamics along and across the magnetic field must be treated separately. On one hand, the resolution must be much higher across the magnetic field than along it. On the other hand, parallel dynamics is typically much faster. Therefore, the two require different numerical treatments, and the operators can be tested with the diffusion model.
3 types of time-discretisation are implemented: fully explicit, explicit parallel and implicit perpendicular, or implicit parallel and explicit perpendicular. This allows to showcase the performance of both the 2D (perpendicular) and 3D (parallel, or both parallel and perpendicular) linear solvers available in GRILLIX.